We've always stayed at one of the Disney hotels until this last trip (last week). We stayed one night at the Candy Cane, 2 nights at Paradise Pier and 2 nights at the Best Western Park Place. This was a bit of an experimental trip to check out staying "offsite".
We didn't arrive at the Candy Cane until 5 pm and left their lot the next morning by 7:30 am so I am not sure what their policy is.
For the Paradise Pier (Disney hotel), you can check in and park early in the morning but most likely, your room won't be ready until later. We left the Candy Cane by 7:30, drove over the PP. We parked and checked in and they gave us a number to call with a pin code to check when our room was ready. We went to the parks and by the time we were ready to come back to our room, the room was ready. The parking pass at PP is good until mid-night of the day you check out. They allow 2 cars per room.
For the BWPPI, they don't let you park until after check-in (3pm) and your parking pass is only good until 3 pm on the day you check-out. Their parking is very tight and they allow only one car per room. We left our car at the PP and then moved over to the BWPPI later in the day (don't remember for sure...probably around 5ish). When we parked, there was only one open spot!
I don't know if other neighboring hotels are similar - I would guess that some of the bigger ones that are a little farther might have bigger parking lots and not be so strict. But, the BWPPI is not a good one for trying to park early and leave the car late.
The Disney hotels are very flexible with their parking - they probably want you there as early as possible and stay as long as possible and since they have the room in their lots, they allow you to park for more extended hours!
When you call for reservations at the hotel you're thinking about, ask what their parking rule is for early/late. Most are pretty strict about the room checkout but might be more flexible with parking.
KC